Fully autonomous vehicles promise enormous gains in safety, efficiency, and economy for transportation. However, before such gains can be realized, a plethora of safety and reliability concerns must be addressed. In previous work, we have introduced a system for managing autonomous vehicles at intersections that is capable of handling more vehicles and causing fewer delays than modern-day mechanisms such as traffic lights and stop signs. While the system is safe under normal operating conditions, we have not discussed the possibility or implications of unforeseen mechanical failures. Because the system orchestrates such precarious ``close calls'' the tolerance for such errors is very low. In this paper, we make four main contributions. First, we introduce safety features of the system designed to deal with these types of failures. Second, we perform a basic failure mode analysis, demonstrating that without these features, the system is unsuitable for deployment due to a propensity for catastrophic failure modes. Third, we give extensive empirical evidence suggesting that not only is this method effective, but that it is so even when normal communications are disrupted. Finally, we provide an analysis of the data indicating that despite the apparent potential for disastrous accidents, autonomous intersection management is likely to improve driver safety considerably.